Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
244 conjugacy classes of subgroups; only the 80 normal subgroups are shown.
This group has 244 conjugacy classes of subgroups — too many to draw. Only its 80 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 3. #10620895 | C2 | semidirect |
| 4. C7×#817 | C2 | semidirect |
| 5. C3×C8×Dic7 | C2 | semidirect |
| 6. #10620510 | C2 | semidirect |
| 13. #66623 | C4 | semidirect |
| 25. C8×Dic7 | D3 | semidirect |
| 35. Dic42 | C2×C4 | semidirect |
| 41. C3×C7×C8 | C2×C4 | semidirect |
| 60. #817 | D7 | semidirect |
| 70. C3×Dic7 | SD16 | semidirect |
| 86. C7×C8 | C4×D3 | semidirect |
| 121. Dic7 | #204 | semidirect |
| 135. C3×C8 | C4×D7 | semidirect |
| 136. C3×C7 | C4×SD16 | semidirect |
| 177. C8 | D21⋊C4 | semidirect |
| 178. C7 | C4×#204 | semidirect |
| 194. C3 | #89624 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#66623 | 2 |
| #10620980 | 2 |
| #10620895 | 2 |
| C7×#817 | 2 |
| C3×C8×Dic7 | 2 |
| #10620510 | 2 |
| #10620504 | 2 |
| #89624 | 3 |
| C4×#204 | 7 |